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A Part is a magnitude of a magnitude ,
the lesser magnitude of the greater magnitude
When Laid down onto  it measures the greater
Thus a Multiple Form  is the greater form
Made of the lesser forms
When laid down it is measured by the lesser forms.

Logos is two homogenous magnitudes Which apply to determining the stage of development of a specific make of sketch form

Let Logos be Magnitudes" placed relative to each other" let's say,
which generating magnitudes we "form into Multiple Forms "  ( placed) relative to one another,letting be bigger and bigger magnitudes.

http://perseus.uchicago.edu/cgi-bin/philologic/getobject.pl?c.31:3:35.LSJ
And following entries. Peelikotees is an interrogative form, and therefore the noun form is nominalising a questioning activity.

In the case of "the  same  logoi"  magnitudes let be  declared :  the first placed near to the second and the third  placed  near to the fourth,
when the magnitude of the first and the third is  a dualled / duplicate multiple form  ,  to  the dualled/ duplicate  multiple form of the second and fourth ,
 That is :
Applied onto the picked out one of the singled out ones
applied onto any specifically numbered multiple form of it.
And the both exceeds or the both duals or the both  falls short Of the taken /picked  one (when ) laid down together.
Thus that case of  "the same logos" magnitudes existing shall be called AnaLogos.


 
[ the first statements of each book are definitions which are general. The general definitions make no sense without specific examples . The specific examples follow in the text and in point of fact are prior to the definitions! However the style is to pronounce the general form or principle drawn from experience like those given in the examples and then to give specific examples that reinforce and illustrate the general principle.
Thus any student moves from not knowing to knowing terminology that is meaningless to attaching meaning to the terminology to appreciating the thought pattern being illicitrd.
When this happens the student is initiated into the jargon of the senior level of discourse. A junior is not only evident by the use of unfamiliar terminology  but also by the lack of ability to demonstrate examples of the terminology, and finally by not demonstrating the thought pattern used in the discourse.

What if the thought pattern is " wrong" ? This can not be the case unless wrong means the pattern does not do what it is claimed it does. Thus if a logos is claimed to give eternal life then it is wrong but a logos is a particular pattern of 2 magnitudes which is used to generate multiple forms to determine the stage of development of a sketch of lines or flat shapes or solids , these latter 2 are dealt with in books 6 and 7
What I need to know : what are these dualled multiple forms
What is Skesis ?
What are the 2 homogenous magnitudes
When are 2 logoi declared the same?
What have to be taken together
What are both and what do they exceed,dual or fall short of ? ]

The first demonstration shows lines as magnitudes , it shows the generating magnitudes  and it shows the multiple forms generated by dualed multiple forming . In this case the dual is the same number of magnitudes forming each respective. Multiple form

Visually it is graspable, verbally it is convoluted! The ear , eye and thought are patterned to apprehend the same thing
A logos is 2 magnitudes treated as a single pattern
The relationships between magnitudes related in this way  is what is being explored .  The first demonstration is that multiple forms generated by the logos are dualled forms , that is the same or a dual number of magnitudes goes into each multiple form
If you know the relationship of one then you know the relationship of the other because they are dualled.
A logos is a pairing of any kind of magnitudes whatsoever? Strictly no , but the principles work for such Inhomogenous pairings.

As I meditate on this I recognise that Monas is not a number . It is anything that we wish to call a unit , a whole entire. Even if it may be constructed from smaller units like Arithmoi generally are, we subsume those into a new Monas or unit.
This is not the same as unity of parts, rather constituents of a unity may be inharmonious  either in behaviour, aesthetics or shape, but we by force of will and convention, even convenience and custom declare them to be a unit, and thusly unify them!!

The notion of a Metron is a secondary layer added to some topological form we clearly declare a unit. The Metron derives it's meaning from a song and dance process called katameetresee, in which we place down a unit while declaring or naming or singing a sound unique to that unit . But unique only in order in which we choose to proceed to sing !
Once laid down, the Arithmos is complete. But we may understand that this process of creating a perfect Arithmos require us to use a process of factorising.
We always factor a larger by a smaller topological form . Thus in a process where forms are at first not commensurable, being either too many Or too little by a unit , that is perisos( as opposed to artios that is perfect fit)  the Euclidean used the remainder to factor the whole thus they inverte the process by maintaining the rule: the smaller into the larger.
This inversion continues until a perfect fit is found. That smallest remainder that does that thing is now the unit of commensurability for the 2 initial topological forms.
But sometimes that remainder can not be found, and then the initial forms are said to be incommensurable.

The ratios and proportions of book 5 explore these relationships between topological forms by analysing it in terms of extensible magnitudes.

The layout for this exploration uses order( first second third and fourth etc) to keep track of the inversions in this process.
From this layout, much later a Persian geometer constructed the rules for a system we call fractions.

While fractions are purveyed as less than wholes, this is not the case. They are proportions and ratios of smaller units of one sort into larger units of another. Or more generally a lesser topological form into a greater topological form .
The ratios and proportions remain the same as laid out in books 5 to 7 of the Stoikeia

It is of great interest to note that from the outset these ratios and proportions deal with the dynamic process of stage development and how to depict it using recognised topological forms sketched in lines by the imagination of an artist ( Skesis)

The etymology of Skesis, and linear B  reveals the link to Aramaic, and the nearveasternnsemitic languages. In these languages the bilateral and trilateral root is important. The root "sk"  root is associated with the hand and all it's functions .
The main function is to hold
The secondary function is with the hold to manipulate what is held, and the third aspect is to depict outcomes of the first 2 processes.

Skazo means to slit by hand ( to loose something)
Then the sk words up to skesis have to do with holding , retaining by being near to hand , being hand made, hand tooled , hand drawn , held in position, shape or form So ribs are like fingers holding in the viscera, and also holding the form
The raft is a rough handmade form, binding together wood and Bouyant materials into a stable form .
All of these ideas feed into the generl notion of a skesis. Thus a Skesis is a fixed form made by hand . Normally the hand element is way in the background , but in this context where the performer is doing a lot of creative processes, the hand element comes to the fore

The idea of a sketch is seemingly tenuous, but it refers to the habit of geometers or rather Astrologers to sketch out the problem or situation either on paper or on the ground.

It is apparent now that Verhältnisse is the German equivalent of Skesis, it being the everyway holded ness in space of some form or conception.